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Answer :
Final answer:
To calculate the mechanical energy lost during the collision with the floor, we need to find the initial and final mechanical energy. The mechanical energy lost is the difference between these two energies. To find the magnitude of the force exerted by the player while dribbling the ball, we need to calculate the work done and divide it by the distance.
Explanation:
(a) To calculate the mechanical energy lost during the collision with the floor, we need to find the initial mechanical energy (potential energy) and the final mechanical energy (rebounding potential energy). The mechanical energy lost during the collision is the difference between these two energies.
Initially, the mechanical energy is given by the formula PE = mgh. Plugging in the values, we have PEinitial = (0.608 kg)(9.8 m/s2)(1.37 m).
After rebounding, the mechanical energy is given by the formula PE = mgh. Plugging in the values, we have PEfinal = (0.608 kg)(9.8 m/s2)(0.626 m).
The mechanical energy lost during the collision is then the difference between these two energies: PEinitial - PEfinal.
(b) To find the magnitude of the force exerted by the player while dribbling the ball, we need to calculate the work done and divide it by the distance. The work done is equal to the force exerted multiplied by the distance.
The work done by the player is given by the formula W = Fd. Plugging in the values, we have W = (F)(0.132 m).
To compensate for the mechanical energy lost during each bounce, the player's work must be equal to the mechanical energy lost during the collision. Therefore, we can set W = PEinitial - PEfinal and solve for the force F.
Learn more about mechanical energy here:
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Answer:
a)[tex]|\Delta E|=4.58\: J[/tex]
b)[tex]F=61.90\: N[/tex]
Explanation:
a)
We can use conservation of energy between these heights.
[tex]\Delta E=mgh_{2}-mgh_{1}=mg(h_{2}-h_{1})[/tex]
[tex]\Delta E=0.608*9.81(0.6026-1.37)[/tex]
Therefore, the lost energy is:
[tex]|\Delta E|=4.58\: J[/tex]
b)
The force acting along the distance create a work, these work is equal to the potential energy.
[tex]W=\Delta E[/tex]
[tex]F*d=mgh[/tex]
Let's solve it for F.
[tex]F=\frac{mgh}{d}[/tex]
[tex]F=\frac{0.608*9.81*1.37}{0.132}[/tex]
Therefore, the force is:
[tex]F=61.90\: N[/tex]
I hope is helps you!
